IsInGroup() not working correctly, can anyone help?

PlayerAdded will not fire for the client that joins the game, but all other clients that join after.

You should be doing this in a server script instead. Here's some sample code:

local Players = game:GetService("Players")
local id = 5150581

Players.PlayerAdded:Connect(function(player)
    -- server will get every player that joins
    if player:IsInGroup(id) then     
    local tool = game.Lighting:WaitForChild("Yoghurt") -- i recommend you put these in ReplicatedStorage or ServerStorage, and NOT Lighting. Lighting is not meant for storage.     

    player.CharacterAdded:Connect(function(char)
        -- gives it to them every character spawn
        tool:Clone().Parent = player.Backpack   
    end)          
    end
end)

Sometimes, while Roblox runs slow the function doesn't process the variable id try just inputting the ID, if neither works then ensure HTTP Requests & API Services are enabled and if still nothing works just wait it out a bit.

local id = 5150581--we can keep this variable outside since it wont update anyway
game.Players.PlayerAdded:Connect(function(player)
    player.CharacterAdded:Connect(function()--wait for the character to load so it knows who to check on, this will update every time a new character gets added instead of a new player

         if player:IsInGroup(id) then   --and here u check if they are in the group since this will get checked after the character gets added                
                game.ServerStorage:WaitForChild("Yoghurt"):Clone().Parent = player:WaitForChild("Backpack")   --if u dont clone it then it will only work once because ur not creating a duplicate, also the backpack gets deleted every time the player dies and recreated so wait for the backpack to be created too
            end
    end)
end)